2022/05/24 by Yang, Jun, Łatuszyński, Krzysztof, Roberts, Gareth O. · 1 citation
#Computation (stat.CO) #FOS: Computer and information sciences #Machine Learning (stat.ML) #Methodology (stat.ME)
paper · doi:10.48550/arxiv.2205.12112
High-dimensional distributions, especially those with heavy tails, are notoriously difficult for off-the-shelf MCMC samplers: the combination of unbounded state spaces, diminishing gradient information, and local moves results in empirically observed ``stickiness'' and poor theoretical mixing properties -- lack of geometric ergodicity. In this paper, we introduce a new class of MCMC samplers that map the original high-dimensional problem in Euclidean space onto a sphere and remedy these notorious mixing problems. In particular, we develop random-walk Metropolis type algorithms as well as versions of the Bouncy Particle Sampler that are uniformly ergodic for a large class of light and heavy-tailed distributions and also empirically exhibit rapid convergence in high dimensions. In the best scenario, the proposed samplers can enjoy the ``blessings of dimensionality'' that the convergence is faster in higher dimensions.